1 community dental health jan ladas. algonquin college - jan ladas2 biostatistics continued...

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COMMUNITY DENTAL COMMUNITY DENTAL HEALTHHEALTH

Jan Ladas

Algonquin College - Jan Ladas 2

BIOSTATISTICS CONTINUEDBIOSTATISTICS CONTINUED

Previously discussed: Descriptive statistical techniques The first measures of spread / central tendency

Information about central tendency is important. Equally important is information about the spread of data in a set.


VARIABILITY/DISPERSIONVARIABILITY/DISPERSION

Three terms associated with variability / dispersion:

Range Variance Standard Deviation

(They describe the spread around the central tendency)



Range:

The numerical difference between the highest and lowest scores

Subtract the lowest score from the highest score

i.e.: c = {19, 21, 73, 4, 102, 88}

Range = 102 – 4 = 98

n.b.: easy to find but unreliable



Variance:The measure of average deviation or spread of scores

around the mean- Based on each score in the set

Calculation:1. Obtain the mean of the distribution2. Subtract the mean from each score to obtain a

deviation score3. Square each deviation score4. Add the squared deviation scores5. Divide the sum of the squared deviation scores by the

number of subjects in the sample



Standard Deviation of a set of scores is the positive square root of the variance

- a number which tells how much the data is spread around its mean

Interpretation of Variance and Standard Deviation is always equal to the square root of the variance

“The greater the dispersion around the mean of the distribution, the greater the standard deviation and variance”


KURTOSISKURTOSIS

Kurtosis of a data set relates to how tall and thin, or short and flat the data set is.

Leptokurtic = tall and thin Mesokurtic = normal, about average Platykurtic = short and flat


NORMAL CURVE (BELL)NORMAL CURVE (BELL)

A population distribution which appears very commonly in life science

Bell-shaped curve that is symmetrical around the mean of the distribution

Called “normal” because its shape occurs so often May vary from narrow (pointy) to wide (flat)

distribution The mean of the distribution is the focal point from

which all assumptions may be made Think in terms of percentages – easier to interpret the

distribution


THE NORMAL CURVETHE NORMAL CURVE

Most used frequency distributions in biostatistics.

Characteristics:

1. Total area under the curve is equal to 1.00 or 100%

2. Mean = mode = median

3. The area under the curve is broken into equal segments which are one standard deviation in width

4. The proportion of area under the curve between:

A the mean and 1 SD (+ or -) 34.13%

B the 1st and 2nd SD 13.59%

C the 2nd and 3rd SD 2.21%


RESEARCH TECHNIQUESRESEARCH TECHNIQUES

Inferential Statistics

(Statistical Inference) Techniques used to provide a basis for

generalizing about the probable characteristics of a large group when only a portion of the group is studied

The mathematic result can be applied to larger population


DEFINITIONS RELATING TO DEFINITIONS RELATING TO RESEARCH TECHNIQUESRESEARCH TECHNIQUES

Population: Entire group of people, items, materials, etc. with at least

one basic defined characteristic in common Contains all subjects of interest A complete set of actual or potential observations

e.g. all Ontario dentists or all brands of toothpasteSample: A subset (representative portion) of the population Do not have exactly the same characteristics as the

population but can be made truly representative by using probability sampling methods and by using an adequate sample size (5 types of “sampling”)



Parameters: Numerical descriptive measures of a population

obtained by collecting a specific piece of information from each member of the population

Number inferred from sample statistics

E.G.: 2,000 women over age 50 with heart disease



Statistic: A number describing a sample characteristic.

Results from manipulation of sample data according to certain specified procedures

A characteristic of a sample chosen for study from the larger population

e.g.: 210 women out of 500 with diabetes have heart problems



Statistics: Characteristics of samples used to infer

parameters (characteristics of populations) A set of tools for collecting / organizing,

presenting and analyzing numerical facts or observations

Survey: The process of collecting descriptive data from a

population


SAMPLING PROCEDURESSAMPLING PROCEDURES

5 Types of Samples:1. A random sample – by chance2. A stratified sample – categorized then

random3. A systematic sample – every nth item4. A judgment sample – prior knowledge5. A convenience sample – readily available


RANDOM SAMPLERANDOM SAMPLE

1. A random sample is one in which every element in the population has an equal and independent chance of being selected. This method is preferred when possible because it equalizes the effect of variables not under investigation but which may influence the observations. It also controls possible selection bias on the part of the researcher.

Sample = 1000 / 5000 students from 50 universities Lottery numbers or names in a hat


STRATIFIED RANDOM STRATIFIED RANDOM SAMPLESAMPLE

12. Stratified random sampling is employed when it may be necessary to select elements of the population according to certain sub groups or categories e.G. Age or gender. This method allows for the control of the variable on which categorization is made. Sample subjects are then randomly chosen from the population making up each category.

E.G.: List of names per university – random selection 1/5 of names


SYSTEMATIC SAMPLESYSTEMATIC SAMPLE

3. Systematic samples are selected by deciding to observe every nth item in the population. This method is not random because not every element in the population has an equal and independent chance for selection.

Every 5th from a list – odd or even numbers


JUDGEMENT SAMPLEJUDGEMENT SAMPLE

4. A judgement sample has characteristics similar to that of a stratified random sample. It is sample selection done when the researcher, with prior knowledge of the population or question under investigation, arbitrarily chooses certain criteria for representation E.G.: Income, educational levels, place of residence etc.

Could be biased.


CONVENIENCE SAMPLECONVENIENCE SAMPLE

5. A convenience sample is chosen because it is most readily available. It may or may not be representative of the larger population. Convenience samples are often chosen on the basis of geographical accessibility.

Reliability is questionable – could be biased.


VARIABLESVARIABLES

The items of a study that are measured.Independent Variable(s) (intervention): All the factors that influence the characteristics

which are under investigation Some of the Independent Variables will be

manipulated as part of the study or experiment = “controlled”i.e.: age, gender, type of oral hygiene aid, amount of drug administered


VARIABLESVARIABLES

Independent Variable(s) (intervention):“Uncontrolled” variables can not be manipulated: Subject’s prior experience Subject’s knowledge base Subject’s emotional state Subject’s values, beliefs

i.e.: dental hygienist evaluating tooth brushing method for children = “controlled variable”


VARIABLESVARIABLES

Dependant Variable(s) The measurable result or outcome which the researcher

hopes will change or not change as a result of the intervention

Their values are determined by all of the independent variables operational at the time of the study (both controlled and uncontrolled)n.b.: called dependant because result depends on independent variablee.g.: subject’s plaque scores / gingival condition

(measured before and after)Result depends on method used.


POTENTIAL PATHOGENS ON POTENTIAL PATHOGENS ON NON-STERILE GLOVESNON-STERILE GLOVES

1. Method = experimental

- Brief outline of experiment

2. Independent variables = items of a study that are measured = the intervention

3. - Gloves – material and origin

- Petri dishes with growth substances

- Time and temperature of incubation

- Testing methods for identification

- Soap – type, amount and use

- Air exposure etc.


POTENTIAL PATHOGENS ON POTENTIAL PATHOGENS ON NON-STERILE GLOVESNON-STERILE GLOVES

Dependant = measurable result

= The types and numbers of micro-organisms found on the tested gloves


CONCEPT OF CONCEPT OF SIGNIFICANCESIGNIFICANCE

Probability – P (symbol)

When using inferential statistics, we often deal with statistical probability.

The expected relative frequency of a particular outcome by chance or likelihood of something occurring

Coin toss


PROBABILITYPROBABILITY

Rules of probability:

1. The (P) of any one event occurring is some value from 0 to 1 inclusive

2. The sum of all possible events in an experiment must equal 1

* Numerical values can never be negative nor greater than 1

0 = non event

P 1 = event will always happen


PROBABILITYPROBABILITY

Calculating probability:

Number of possible successful outcomes

/ Number of all possible outcomes

E.G.: Coin flip:

1 successful outcome of heads

/ 2 possible outcomes = P = .5 or 50%

E.G.: Throw of dice

1 successful outcome

/ 6 possible outcomes = P = .17 or 16.6%


HYPOTHESIS TESTINGHYPOTHESIS TESTING

The first step in determining statistical significance is to establish a hypothesis

To answer questions about differences or to test credibility about a statement

e.g.: ? – does brand X toothpaste really whiten teeth more than brand Y ?


HYPOTHESIS TESTINGHYPOTHESIS TESTING

Null hypothesis (Ho) = there is no statistically significant difference between brand X and brand Y

Positive hypothesis = brand X does whiten more* Ho – most often used as the hypothesis* Ho – assumed to be true

Therefore the purpose of most research is to examine the truth of a theory or the effectiveness of a procedure and make them seem more or less likely!


HYPOTHESIS HYPOTHESIS CHARACTERISTICSCHARACTERISTICS

Hypothesis must have these characteristics in order to be researchable.

Feasible Adequate number of subjects Adequate technical expertise Affordable in time and money Manageable in scope

Interesting to the investigator

Novel Confirms or refutes previous findings Extends previous findings Provides new findings


HYPOTHESIS HYPOTHESIS CHARACTERISTICSCHARACTERISTICS

Ethical

Relevant To scientific knowledge To clinical and health policy To future research direction


SIGNIFICANCE LEVELSIGNIFICANCE LEVEL

A number (a = alpha) that acts as a cut-off point below which, we agree that a difference exists = Ho is rejected. Alpha is almost always either 0.01, 0.05 or 0.10.

Represents the amount of risk we are willing to take of being wrong in our conclusion

P < 0.10 = 10% chanceP < 0.01 = 1% chance (cautious)P < 0.05 = 5% chance

Critical value cut-off point of sample is set before conducting the study (usually P < 0.05)


ERRORSERRORS

Type I (Alpha): Is made when we reject the null hypothesis

when, in fact, it is true, therefore could lead to practicing worthless treatments that do not work.

Type II (Beta): Is made when we do not reject the null

hypothesis when, in fact, it is false, therefore could lead to overlooking a promising treatment.

e.g.: the law – “innocent” or “guilty”


DEGREE OF FREEDOM DEGREE OF FREEDOM (d.f.)(d.f.)

Most tests for statistical significance require application of concept of d.f.

d.f. refers to number of values observed which are free to vary after we have placed certain restrictions on the data collected

* d.f. usually equals the sample size minus 1

e.g.: 8, 2, 15, 10, 15, 7, 3, 12, 15, 13 = 100

d.f. = number (10) minus 1 = 9 Takes chance into consideration A penalty for uncertainty, so the larger the sample the

less the penalty

1 community dental health jan ladas. algonquin college - jan ladas2 biostatistics continued...

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